Abstract
The shear viscosity is an important characterization of how a many-body system behaves like a fluid. We study the shear viscosity in a strongly interacting solvable model, consisting of coupled Sachdev-Ye-Kitaev (SYK) islands. As temperature is lowered, the model exhibits a crossover from an incoherent metal with local criticality to a marginal fermi liquid. We find that while the ratio of shear viscosity to entropy density in the marginal Fermi liquid regime satisfies a Kovtun-Son-Starinets (KSS) like bound, it can strongly violate the KSS bound in a robust temperature range of the incoherent metal regime, implying a nearly perfect fluidity of the coupled local critical SYK model. Furthermore, this model also provides the first translationally invariant example violating the KSS bound with known gauge-gravity correspondence.
Highlights
Fluid mechanics is among the oldest and the most fundamental subjects in physics
Though a similar violation of the KSS bound is reported in unitary quantum gases by dynamic mean field theory calculation [35], the SYK model has a better holographic interpretation [39,42] and analytical controllability than the model used in Ref. [35]
Our calculations provide the first translationally invariant example violating the KSS bound with known gauge-gravity correspondence
Summary
Fluid mechanics is among the oldest and the most fundamental subjects in physics. A generic many-body system with globally conserved quantities, such as mass, energy, and momentum, will exhibit fluidity if the local thermalization time scale is much less than the relaxation time scale of the conserved quantities. When rotational symmetry is broken, like the anisotropic black branes [15,16,17], certain component of shear viscosity tensor may violate the KSS bound in a parametric manner which was recently illustrated in an anisotropic Dirac fluid [18]. The minimal of the ratio occurs at an intermediate temperature range associated with the superfluid transition, providing possible examples violating the KSS bound [35], while at the zero-temperature limit the gapless Goldstone modes lead to a divergent ratio. The ratio can strongly violate the KSS bound in a robust temperature range of the IM regime, implying a nearly perfect fluidity of the coupled local critical SYK models, and providing the first translationally and rotationally invariant example violating the KSS bound with known gauge-gravity correspondence
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